Imagine preparing two networks A & B of trapped ionsspacelike separated from each other with Glaubercoherent states |z) in their nano-meter COM mechanical phonon oscillations entangled with their internal Jaynes-Cummings qubits |1(0)). Then do an entanglement swap between the Jaynes-Cummingsinternal bit networks. Sure this will take light cone limited classical time delay to accomplish, but once that is finished then the nonlocal superluminalcommunication can begin to be tested - evenretrocausally.
The initial preparation is the Schrodinger Cat entangled state
z = (n)^1/2e^i@(coherent)
|Az)|A1) + |Az*)|A0)X(|Bz)|B1) + |Bz*)|B0))
tensor product of Hilbert spaces
after the entanglement swap (inside respective light cones)
the new state ready for nonlocal entanglement signaling is
|Az)|B1) + |Az*)|B0)X(|Bz)|A1) + |Bz*)|A0))
For example, the receiver signal at B to detect aJaynes-Cummings internal bit “1” will be
S(B1) ~ (1/2)(1 + |(Az|Az*)|^2)
in violation of the Born probability rule because of the “More is different” (P.W. Anderson) phase rigidity of the nano-mechanical oscillator coherent real phonon (center of mass motion) over-complete distinguishable non-orthogonal Glauber states.
It is the Born probability rule that needs to be tested in this situation and not simply assumed apriori
Zeilinger et-al wrote:
"In the entanglement swapping1-3 procedure, two pairs of entangled photons are produced, and one photon from each pair is sent to Victor. The two other photons from each pair are sent to Alice and Bob, respectively. If Victor projects his two photons onto an entangled state, Alice’s and Bob’s photons are entangled although they have never interacted or shared any common past. What might be considered as even more puzzling is Peres’ idea of “delayed-choice for entanglement swapping”4. In this gedanken experiment, Victor is free to choose either to project his two photons onto an entangled state and thus project Alice’s and Bob’s photons onto an entangled state, or to measure them individually and then project Alice’s and Bob’s photons onto a separable state. If Alice and Bob measure their photons’ polarization states before Victor makes his choice and projects his two photons either onto an entangled state or onto a separable state, it implies that whether their two photons are entangled (showing quantum correlations) or separable (showing classical correlations) can be defined after they have been measured. In order to experimentally realize Peres’ gedanken experiment, we place Victor’s choice and measurement in the time-like future of Alice’s and Bob’s measurements, providing a “delayed-choice” configuration in any and all reference frames" - end quote
Unfortunately, for trapped ions the nanomechanical phonon coherent state is physically attached to the internal Jaynes-Cummings bit so we cannot send one to Victor. We would need an additional step, teleporting the Jaynes-Cummings bit to another two level system that could be physically moved to Victor.
It’s not yet clear to me if this could be done keeping the basic initial entanglement pattern using the trapped ions. However, there may be some other more suitable way of implementing the basic idea.
Experimental delayed-choice entanglement swapping
Xiao-song Ma1,2, Stefan Zotter1, Johannes Kofler1,a,
Rupert Ursin1, Thomas Jennewein1,b, ?aslav Brukner1,3, and Anton Zeilinger1,2,3
1 Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
2 Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
3 Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
a Present Address: Max Planck Institute of Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching/Munich, Germany
b Present Address: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Ave W., Waterloo, ON, Canada N2L3G1
Motivated by the question, which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayed-choice entanglement swapping. There, entanglement can be “produced a posteriori, after the entangled particles have been measured and may no longer exist.” In this work we report the first realization of Peres’ gedanken experiment. Using four photons, we can actively delay the choice of measurement – implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator – on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as “quantum steering into the past”.